MAJOR BUG FIXED. x domain now starts at zero. pdepe enforces no-flux for...

MAJOR BUG FIXED. x domain now starts at zero. pdepe enforces no-flux for spherical coordinates at absolute zero, not at the beginning of the domain.

ternary_frap.m

@@ -2,26 +2,24 @@
 % unbleached species. Model is assumed to be equilibrated
 % (bleached+unbleached=const.=pt). Then bleached species initial
 % conditions are introduced. Integration of model via pdepe.
-
-a = -50;
+pa = '/Users/hubatsch/ownCloud/Dropbox_Lars_Christoph/DropletFRAP/FRAP_paper/';
+a = -1;
 b = 0.025;
 c = 1/100;
 u0 = 0.05;
 e = 0.4;
 
 %% Make useful mesh (by inverting the tanh profile and using this as spacing)
-x = linspace(49.0, 51, 3000);
+x = linspace(-a-1, -a+1, 3000);
 g = gamma0(x, a, 1*b, e);
 g_unique = unique(g);
 x = linspace(g_unique(1), g_unique(end-1), 300);
 g_inv = spacing(x, a, 2*b, e);
 g_inv = g_inv(2:end-1);
-x = [linspace(49.0, g_inv(2), 30), g_inv(3:end-2), ...
-    linspace(g_inv(end-1), 51, 30), linspace(51.1, 300, 300)];
+x = [linspace(-a-1, g_inv(2), 30), g_inv(3:end-2), ...
+    linspace(g_inv(end-1), -a+1, 30), linspace(-a+1.1, 300, 300)];
 %% Solve pde
 tic
-% x = [linspace(49.0, 49.8, 30), linspace(49.81, 50.2, 1000), ...
-%      linspace(50.21, 51, 30) linspace(51.01, 200, 600)];
 t = linspace(0.001, 4, 500);
 fh_ic = @(x) flory_ic(x, a, u0);
 fh_bc = @(xl, ul, xr, ur, t) flory_bc(xl, ul, xr, ur, t, u0);
@@ -31,7 +29,7 @@ toc
 %% Plotting
 figure(1); hold on;
 for i = 1:length(t)
-    cla; xlim([49, 53]); ylim([0, 0.7]); 
+    cla; xlim([-a-1, -a+3]); ylim([0, 0.7]); 
     ax = gca;
     ax.FontSize = 16;
     xlabel('position'); ylabel('volume fraction');
@@ -46,9 +44,10 @@ xlim([49, 53]); ylim([0, 0.5]);
 ax = gca;
 ax.FontSize = 16;
 xlabel('position'); ylabel('volume fraction'); 
-plot(x, sol(1:2:300, :), 'LineWidth', 2, 'Color', [135/255  204/255 250/255]);%[0    0.4470    0.7410]
-plot(x, phi_tot(x, a, b, e, u0), 'LineWidth', 4, 'LineStyle', '--', 'Color', [247/255, 139/255, 7/255]);
-print('/Users/hubatsch/ownCloud/Dropbox_Lars_Christoph/DropletFRAP/FRAP_paper/ternary_time_course', '-depsc');
+plot(x, sol(1:2:300, :), 'LineWidth', 2, 'Color', [135/255  204/255 250/255]);
+plot(x, phi_tot(x, a, b, e, u0), 'LineWidth', 4, 'LineStyle', '--', 'Color',...
+    [247/255, 139/255, 7/255]);
+print([pa, 'ternary_time_course'], '-depsc');
 %% Plot and check derivatives of pt
 figure; hold on;
 x = linspace(40, 60, 100000);
@@ -74,9 +73,9 @@ end
 
 function u = flory_ic(x, a, u0)
     % FRAP initial condition
-%     if x < -a; u = 0.0; else; u = u0; end
+    if x < -a; u = 0.0; else; u = u0; end
     % Peak outside initial condition
-    if (x < -a+0.2) && (x > -a+0.1); u = 10; else; u = 0; end
+%     if (x < -a+0.2) && (x > -a+0.1); u = 10; else; u = 0; end
 %     u = 0.3;
 %     u = phi_tot(x, -50, 1);
 end